What is the logic behind this prolog code? -

i have short prolog code finds last element of given list.

last_of([_|tail], x) :- last_of(tail, x), !. last_of([x], x). 

but have question logic of program. why use last_of([x], x)., couldn't understand this. can explain?

there several comments program:

1st, name misnomer. first argument list, second last element. name suggests otherwise. better name list_last/2 or last/2.

2nd, cut misplaced. in fact, exchanging rules , removing cut, more efficient, , more declarative:

last([x]   , x). last([_|xs], x) :- last(xs,x). 

now question. when starting programming in prolog, best imagine ground queries first. let's make several examples relation should succeed.

?- last([a],a). 

for true, fact last([a],a). sufficient. can generalize fact last([x],x).. after that, might consider list 2 elements fact last([_,x],x). cover lists of length 2. etc.

last([x],x). last([_,x],x). last([_,_,x],x). ... 

now, let's generalize pattern! lets reduce case of longer list shorter list. this, assume know last element of xs:

????   :-    last(xs, x). 

what can conclude when know x last element of xs? can conclude list longer 1 element have same x last element, too! thus:

last([_|xs], x) :-    list(xs, x). 

so rule, can make list longer , longer. if there case can start from! reason need list([x],x). best add fact first, because find answers goal list(xs, a), too.

please note particular way how looked @ :-. read right-to-left arrow implying new: if goals on right true, goals on left true.

frequently, people try understand prolog rules in way how prolog executes them. , not right-to-left did, left-to-right. however, reading unintuitive humans, since prolog uses quite unusual way execute: on 1 hand uses unification far more complex pattern matching , backtracking. both notions not present in traditional programming languages, thereby confusing more help.